Methods of analyzing cement integrity in annuli of a multiple-cased well using machine learning

ABSTRACT

A sonic tool is activated in a well having multiple casings and annuli surrounding the casing. Detected data is preprocessed using slowness time coherence (STC) processing to obtain STC data. The STC data is provided to a machine learning module which has been trained on labeled STC data. The machine learning module provides an answer product regarding the states of the borehole annuli which may be used to make decision regarding remedial action with respect to the borehole casings. The machine learning module may implement a convolutional neural network (CNN), a support vector machine (SVM), or an auto-encoder.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. 119(e)to U.S. Provisional Patent Application No. 62/577,945, filed Oct. 27,2017, the entire contents of which are incorporated herein by reference.

FIELD

This disclosure relates to well logging in oil and gas fields. Inparticular, this disclosure relates to analyzing the status, forexample, the cement integrity of annuli in a multiple-cased oil and gaswell.

BACKGROUND

Effective diagnosis of well zonal isolation has become important withthe recent advent of harsher governmental regulations that call for oiland gas operators to deliver and maintain wells with competent pressureseals. The goal is to prevent uncontrolled flow of subterraneanformation fluids causing leaks into the atmosphere or into otherformations. See, e.g., “Isolating potential flow zones during wellconstruction,” American Petroleum Institute Recommended Practice, Vol.65-Part 2, 2010. The diagnosis could be carried out following acementation job or during the life of a well or at the end of its lifebefore plug and abandonment.

Acoustic measurements are widely used to diagnose the condition andplacement of the cement and its bond to interfaces in contact with it.The current methods, encompassing high frequency sonic CBL-VDL (See, V.Pistre, et al., “A modular wireline sonic tool for measurements of 3dformation acoustic properties,” SPWLA 46th Annual Logging Symposium,2005) and ultrasonic measurements, are designed for single casingstrings and therefore can be used at best only for the diagnosis of theannulus behind the innermost casing string and the bonds therein.However, in several markets including plug and abandonment, there isincreasing interest in diagnosing the placement and bond of cementbehind more than one string to avoid costly operations of cutting andpulling casing and multiple logging runs. To address this market, thereis a need for additional measurements and/or processing approaches thatleverage the possibility of probing deeper than the first casing andannulus while addressing the challenges of diagnosing the cementplacement behind second casings despite the increased complexity of themeasurement physics in multiple casing strings. Co-owned patentapplications to S. Zeroug, et al., US 20150219780 and to S. Bose et al.,WO/2016US32965A propose a joint diagnosis of multiple acousticmodalities leveraging their independent sensitivities. The anticipatedresult is a more robust diagnosis of the content of the annulus andwhether it provides hydraulic isolation based on quantitative inversionof relevant parameters. The S. Zeroug et al. application proposes amodel-based inversion of the relevant parameters.

In practice, however, continuous logs covering thousands of feet alongthe well must be generated and it may not be feasible with the availablecomputational resources to invert beyond a few selected locations. Forsuch a scenario, to cover the tens of thousands of depth frames, the S.Bose et al. application proposed a different approach of extractingattributes or features from all the available measurements and usingthose in machine learning algorithms to make a categorical diagnosis ofnot only the first annulus but also the annuli and bond conditionsbeyond the second casing. In addition, the sonic measurements are inthemselves quite rich as they include monopole and dipole logging modesthat interrogate the cased hole system in diverse ways, enabling such adiagnosis. Three additional co-owned patent applications to B. Sinha, etal., WO2014/US70255A, and to T. Lei, et al., WO2016/186240 andWO2016/187239 are devoted to techniques employing sonic data for wellintegrity diagnosis. In another co-owned patent application to M.Skataric, et al., WO2017/151834, a methodology is outlined to processand display data over depth intervals with emphasis on features thatindicate discontinuities indicative of such depth dependent transitions.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

This subject disclosure relates to cement barrier integrity in cased oiland gas wells with multiple casing strings.

The subject disclosure outlines an approach for the evaluation of wellintegrity in dual and multi-string casings using sonic data that readsdeeper than the first casing and annulus. The array sonic datacomprising one or more of monopole, dipole and quadrupole modalitiesfrom one or more sources is pre-processed via a transform such as the(normalized) slowness time coherence (STC) transform, or the related(non-normalized) Radon transform into a geophysical meaningful domainsuch as slowness-time domain. The resulting 2-D or 1-D intermediateresults are fed into a machine learning module such as a support vectormachine (SVM), an auto-encoder, or a convolutional neural network (CNN)which has been trained with a training data set having labeled samplesto learn features and discriminators particularly for the state ofannuli behind the casings. The structure of the network is heuristicallydesigned to achieve reliable performance. The output of the machinelearning module is an answer product as to the states of the annulibehind the casings at the depth in the formation from which the arraysonic data was gathered. Data from multiple depths may be used to obtainanswer products at different locations along the wellbore and the answerproducts may be used for determining remedial or other actions to betaken.

BRIEF DESCRIPTION OF DRAWINGS

The subject disclosure is further described in the detailed descriptionwhich follows, in reference to the noted plurality of drawings by way ofnon-limiting examples of the subject disclosure, in which like referencenumerals represent similar parts throughout the several views of thedrawings, and wherein:

FIG. 1 is a high-level flow-chart of disclosed methods for analyzingannuli of a multiple-cased well using machine learning;

FIGS. 1a and 1b depict a wireline Sonic Scanner tool, showing thetransmitters and receiver array and cross-dipole firings;

FIG. 2 is a depiction of a sonic tool located in a multiple-casingstring well;

FIGS. 3a and 3b respectively depict monopole and dipole modalitiesexcited by a Sonic Scanner™ tool, together with their waveforms anddirection of source firing;

FIG. 4 depicts a synthetic dataset showing a training set encompassingfive possible cases of fill in annulus A and B on the left and two testset scenarios on the right for evaluating the classification performanceof the algorithm;

FIG. 5 shows training and testing datasets;

FIGS. 6a and 6b respectively depict Butterworth filters (bands) withdifferent cutoff frequencies on a normalized frequency scale and on anoriginal frequency scale;

FIGS. 7a-7d respectively depict a sonic acquisition tool acquiring data,the receiver data as a function of receiver and time, an STCtwo-dimensional (2D) image, and an STC one-dimensional image obtainedfrom a projection of the STC 2D image;

FIG. 8 is a classification result using SVM on unlabeled full frequencyband monopole data (Scenario 1);

FIG. 9 is a classification result using SVM on unlabeled full frequencyband monopole data (Scenario 2);

FIG. 10 is a classification result using SVM on unlabeled full frequencyband dipole data (Scenario 1);

FIG. 11 is a classification result using SVM on unlabeled full frequencyband dipole data (Scenario 2);

FIG. 12 is a classification result using SVM on unlabeled multiband data(Scenario 1) where M1, and M2 denote monopole data in frequency rangesBPF1, and BPF2; D1, D2, D3, denote dipole data in frequency ranges BPF1,BPF2, and BPF3; M denotes combined monopole frequency bands; D denotescombined dipole frequency bands, and MD denotes combined monopole anddipole frequency bands;

FIG. 13 is a classification result using SVM on unlabeled multiband data(Scenario 2) where M1, and M2 denote monopole data in frequency rangesBPF1, and BPF2; D1, D2, D3, denote dipole data in frequency ranges BPF1,BPF2, and BPF3; M denotes combined monopole frequency bands; D denotescombined dipole frequency bands, and MD denotes combined monopole anddipole frequency bands;

FIG. 14 is a schematic of a convolutional auto-encoder;

FIG. 15 depicts parameters of the auto-encoder of FIG. 14;

FIGS. 16a-16e show learned bottleneck features with the x-axis being thepixel index of the bottleneck feature, and the y-axis representing thetraining set index;

FIG. 17 is a training/testing diagram of auto-encoder with SVM;

FIG. 18 is a cross validation diagram of auto-encoder with SVM;

FIG. 19 shows original and reconstructed STC 2D images for label 1(Cubes 1 through 250) for Cube #25;

FIG. 20 shows original and reconstructed STC 2D images for label 2(Cubes 151-300) for Cube #201;

FIG. 21 shows original and reconstructed STC 2D images for label 3(Cubes 301-450) for Cube #325;

FIG. 22 shows original and reconstructed STC 2D images for label 4(Cubes 451-600) for Cube #476;

FIG. 23 shows original and reconstructed STC 2D images for label 5(Cubes 601-750) for Cube #667;

FIG. 24 shows a classification result using auto-encoding plus SVM(AE+SVM) on unlabeled multiband multimodality data (Scenario 1) wherethe data used is as given on FIG. 12;

FIG. 25 shows a classification result using AE+SVM on unlabeledmultiband multimodality data (Scenario 2) where the data used is asgiven on FIG. 13;

FIGS. 26a-26h depict support vectors corresponding to various multibandmodalities for five labels of interest;

FIG. 27 depict Mel-frequency cepstral coefficient (MFCC) methods;

FIGS. 28a and 28b respectively depict convolutional neural network (CNN)parameters for monopole and dipole data;

FIG. 29 depicts dimensions of single stream CNN (dipole input);

FIGS. 30a and 30b respectively depict STC 2D images (3 dipole bands)used in generating the activation maps, and filter weights computed fromthe first convolution stage;

FIGS. 31a and 31b respectively depict activation maps for dipole inputsafter a CONV1 layer and after a CONV2 layer;

FIGS. 32a and 32b respectively depicts STC 2D images (2 monopole bands)used in generating the activation maps, and filter weights computed fromthe first convolution operation;

FIGS. 33a and 33b respectively depict monopole activation maps after aCONV1 layer and after a CONV2 layer;

FIGS. 34a-34c are two stream CNN frameworks for combining results frommonopole and dipole data; and

FIGS. 35a and 35b depict classification of multiband multimodality datafrom Scenario 1 & 2 using CNN methods, with the first panel of bothFIGS. 35a and 35b showing classification using two band monopole data,the second panel showing classification results using three band dipoledata, and the last three panels showing three methods for combining twostreams of data, respectively.

DETAILED DESCRIPTION

The particulars shown herein are by way of example and for purposes ofillustrative discussion of the embodiments of the subject disclosureonly and are presented in the cause of providing what is believed to bethe most useful and readily understood description of the principles andconceptual aspects of the subject disclosure. In this regard, no attemptis made to show structural details in more detail than is necessary forthe fundamental understanding of the subject disclosure, the descriptiontaken with the drawings making apparent to those skilled in the art howthe several forms of the subject disclosure may be embodied in practice.Furthermore, like reference numbers and designations in the variousdrawings indicate like elements.

In the subject disclosure, machine learning approaches are presented toextract and train on features of sonic data over depth using any of avariety of algorithms to identify several proposed classes for twoannuli (“annulus A” and “annulus B”) given the availability of data withlabels for those classes. Thus, as suggested in FIG. 1, at 100, 102,104, 106, and 108, a machine learning module is trained with a trainingdata set having labeled samples to learn features and discriminators forthe state of annuli behind casings of a wellbore. More particularly, at100, sonic data is collected or synthesized with respect to a boreholehaving a plurality of casings with annuli surrounding the casings. Thesonic data that is collected may include one or both of monopole anddipole sonic data. At 102, the sonic data may be divided into multiplefrequency bands, and the data is processed to obtain 2D STCtime-slowness maps or 1D slowness projection vectors. At 104, labels forvarious status conditions of interest of the annuli surrounding thecasings are generated. The labels and the preprocessed sonic data in theform of the STC maps or vectors are then used at 106 to create atraining dataset of labeled samples of 1D and/or 2D STC outputs for oneor more frequency bands of the monopole and/or dipole data. The trainingdataset is then used to train a machine learning module which receivesand trains on the information. Examples of suitable machine learningmodules include a support vector machine (SVM), an auto-encoder—SVMcombination, or a convolutional neural network (CNN). To ascertainwhether the machine learning module is properly trained, across-validation set of preprocessed STC 2D or projected 1D information(e.g., a portion of the training dataset) may be utilized at 110.Regardless, once the machine learning module is suitably trained, anacoustic borehole tool may be placed at 120 at a location in a boreholehaving a plurality of casings with annuli surrounding the casings, andthe (monopole and/or dipole) transmitter(s) may be activated at 130 sothat acoustic energy is radiated into the casings surrounding theborehole and waveforms are detected at the detectors of the acousticborehole tool. At 140, the detected waveforms are preprocessed usingslowness-time-coherence (STC) processing to obtain a 2D STC map, or a 1DSTC vector projection. At 150, the 2D STC map or 1D STC vectorprojection is provided to the trained machine learning module, and at160, the machine learning module provides an answer product as to thestates of the annuli behind the casings of the wellbore. As suggested inFIG. 1, the borehole tool may be moved at 170 to another location in theborehole where the transmitter(s) may be activated and waveformsdetected at 130, STC processing conducted at 140, and resulting STC mapor vector projection provided to the trained machine learning module at150 so that additional answer product may be generated at 160 for thatlocation in the borehole. The answer products for one or more depths inthe borehole may be used at 180 in a decision regarding the necessity ornot of taking remedial action with respect to the borehole. Thus, by wayof example only, if it is determined that both annuli are not properlycemented in a wellbore which is going to be abandoned, a decision may bemade to remove the casings from the wellbore prior to injecting cementinto and capping the wellbore.

The following disclosure relates to details of implementing aspects ofcertain elements of FIG. 1.

FIG. 1a depicts a wireline tool such as the Sonic Scanner with amultiplicity of transmitters and a 2-D axial and azimuthal array ofreceivers which may be used in conjunction with the activation oftransmitters so that acoustic energy is radiated into the casingssurrounding the borehole and detecting waveforms at the detectors of theacoustic borehole tool at 130. It may also be used in conjunction withthe collection of sonic data at 100 for the purpose of generatingtraining datasets at 106. The Sonic Scanner has the capability ofacquiring wideband sonic modal logging measurements with the signalfrequency ranging from 200 Hz to 12 kHz. In a “Record-All-Data”acquisition mode of the tool, the measurement is very rich in data asmultiple borehole modes are excited and detected using the multipletransmitters and individual recordings of receivers in the 2-D array.These include the monopole mode that can be excited both at low and highfrequencies and with far and near (to the receiver array) monopolesources, and the dipole mode that can be excited at two orthogonaldirections yielding cross-dipole excitation as seen in FIG. 1b . Whilethese sonic measurements have not previously been used for wellintegrity applications and have some of the same limitations such as alack of azimuthal resolution (monopole) or only two quadrant resolution(dipole), low axial resolution (of the order of 1 m), and sensitivity tomultiple mechanisms over the probed region, they have the capability toprobe beyond the first casing and annulus, and therefore bring thecapacity for a diagnosis of the annuli in multiple casingconfigurations. This is particularly true if the inner casing andannulus state are known or determined by another measurement such as thehigh resolution ultrasonic from the Isolation Scanner.

FIG. 2 depicts a typical multiple casing configuration in an oil and gaswell in which the acoustic borehole tool is placed at 120 of FIG. 1. Aseries of casings are deployed inside the wellbore in telescopicfashion. The annulus behind each casing is partially or fully filledwith cement to assure well integrity and zonal isolation of variousformations layers. In some situations, it may be necessary to evaluatethe annular fill and bond in cement behind multiple overlapping casingswith a tool deployed in the fluid filled innermost casing. Examples ofpotential diagnoses of annulus A (behind first casing; i.e., between thefirst and second casings) and annulus B (behind second casing) aredepicted for a dual casing scenario.

In one aspect, in assessing the necessity or desirability of takingremedial action with respect to the borehole, those of skill in the artmay be interested in some or all of the following scenarios or answerproducts (such as are obtained at 160):

1. Full bond (both annuli are cemented);

2. The inner annulus (annulus A) is liquid, and the outer annulus(annulus B) is cemented;

3. Annulus B is liquid, and annulus A is cemented;

4. Both annuli are liquid-filled;

5. Barite sag in one or both annuli; and

6. Partial bond in one or both annuli.

Other scenarios may also be of interest to those of skill in the art.

In one embodiment, the six scenarios are considered for formationshaving distinct types of acoustic properties, such as formations thatare “super-fast”, “fast”, “medium”, and “slow” (all referring to thevelocity of sound waves in the formation), for the purpose ofencompassing a range of possible sonic responses that could provideidentifying features. Typical range values for these formation types aresummarized in Table 1 below, where DT_(c) is the compressional slowness(with slowness being the inverse of velocity), DT_(s) is the shearslowness, and ρ is the formation density. For example, the type offormation (slow vs. fast) imposes constraints on the ranges offrequencies/slownesses in which to search for the distinguishingfeatures as described below. Hence, scenarios or features may be definedwithin a particular formation type, leading to a total of twenty-fourclasses where there are six scenarios and four formation types, (e.g.,double casing with cemented annulus A and liquid annulus B, in a fastformation, etc.). This framework can be extended to deal with partialbond cases in more detail, by determining at which interface thedisbonding occurs. With more scenarios, the number of classes increasesaccordingly.

In the following disclosure, methodologies are described to leveragemachine learning in order to generate an indicator (answer product at160 of FIG. 1) for the onset of a free pipe (i.e., uncemented casing)for one or more strings in the multi-string cased hole. Themethodologies and conclusions are demonstrated on synthetic data. Inaddition, depth dependent displays of dispersion and slowness semblanceprojections for identifying transitions in the annuli in such scenariosare described.

Synthetic Dataset Description

Synthetic data which may be used for training a machine learning modulemay be generated through modeling software (100 of FIG. 1). In oneembodiment, the synthetic data may pertain to measurements obtained by aSonic Scanner tool. Acquired simulated data could be obtained frommonopole and/or dipole sources, with FIGS. 3a and 3b respectivelydepicting monopole and dipole modalities excited by a Sonic Scannertool, together with their waveforms and direction of source firing.

In the posited classification problem, for illustration purposes,classification of two sections encompassing double casing stringscenarios with annulus A and B is considered for the following fivescenarios: (A=Hard cement, B=Hard cement); (A=Lite cement, B=Litecement); (A=Water, B=Hard cement), (A=Water, B=Lite cement), and(A=Water, B=Water). Each scenario is provided as a “label” (104 of FIG.1). For example, the label W-HC corresponds to the third listed scenariowith annulus A (between two casings) being water-filled (W) and annulusB (between the second casing and the formation) having hard cement (HC).The goal is to identify these sections and the transitions. HC, LC, andW may be used to represent hard cement, lite cement, and water,respectively. Thus, as suggested above, the label W-HC may be used toindicate water in annulus A and hard cement in annulus B.

For purposes of illustration, and by way of example only, for each labeland modality (monopole/dipole), twenty-five synthetic sonic data cubes(time, receiver, depth) are generated for the training step in thelearning framework. The nominal values and range of physical propertiescorresponding to each fill and formation type are shown in Table 1.

TABLE 1 Table of acoustic properties with nominal values and ranges forformation types and annular and borehole fill considered for scenariosbeing tested. For purpose of generating synthetics for training, a rangeof values around each nominal value for formation types is used andsampled to mimic typical variation in natural sub-surface formations.FORMATION Type DT_(c) (μs/ft) DT_(s) (μs/ft) ρ (g/cm³) Super fast 62.5 ±10 108.2 ± 20 2.58 ± 0.1 Fast   80 ± 10   160 ± 20  2.3 ± 0.1 Medium 1 100 ± 10   240 ± 20  2.2 ± 0.1 Medium 2  120 ± 10   250 ± 20  2.2 ± 0.1ANNULUS Content DT_(c) (μs/ft) DT_(s) (μs/ft) ρ (g/cm³) Hard Cement 82149 2 Lite Cement 157 406 1.43 Mud in annulus A 260 inf 1.52 Mud inannulus B 220 inf 1.37 Borehole Mud 195 inf 1.2

At each location (corresponding to each data cube), the waveforms aresampled from 30 depth frames, and using a thirteen-receiver array (asshown in FIGS. 1a and 1b ). For each waveform, there are 601 timesamples. For simplicity, only a subset of the generated 25 data cubesare used. The above-mentioned cubes (or runs) of data, after appropriateprocessing (described hereinafter) are used to generate a “labeleddataset”, which are used for training the model (106 of FIG. 1). Thelabeled dataset is subsequently split into a “training set” (108 of FIG.1), used to learn the representation of the data, and a“cross-validation” (CV) Set, that may be used (at 110 of FIG. 1) tocompute the classification accuracy of the trained model, given theunseen new data, for which the exact labels are known as suggested byFIG. 5.

TABLE 2 Scenarios and depth indices used to create Testing dataset.Monopole and Dipole Data Scenario Sample range Label Annulus A Annulus BScene 1 1:65 1 HC HC 66:135 3 W HC 136:200  5 W W Scene 2 1:75 2 LC LC76:125 4 W LC 126:200  5 W W

For testing purposes, two synthetic test sets (referred to here as“Scenario 1” or “Scene 1”, and “Scenario 2” or “Scene 2”) are generated,encompassing both monopole and dipole modalities, and representing datareceived over 200 depth frames. These sets will be referred to as “Testdata”, or “Unlabeled data”. The detailed list of labels and their depthranges for the two scenarios are shown in Table 2. The classificationaccuracy of the learned network may be assessed on the unlabeled (test)datasets since labels have been created for the two scenarios. However,in real applications the network will only have access to the labels fortraining and cross-validation from prior modeling, expert elicitation,or previous data labeling and acquisition.

The “ground truth” labels as a function of depth for the two scenariosof Table 2 are shown in FIG. 4. In the simulations, the formation canvary over a range of slownesses from 100-240 μs/ft to mimic typicalbedding and variation in sub-surface formations.

Data Preprocessing

As previously indicated, the machine learning module is trained with aset of preprocessed acoustic information. Embodiments of datapreprocessing that lead to the specification of the classificationmethods are described hereinafter.

Bandpass Filters

Compared to synthetic data sets, the real data usually contains someartifacts and noise and may not match the ideal conditions of themodeled data. To make classifiers more robust, and to mimic imperfectfield data, data with added noise to the signal (e.g., SNR=1 dB, andSNR=10 dB) may be utilized.

To account for the richness of modes seen in the field data, bandpassfilters are optionally used at 102 of FIG. 1 to preprocess thewaveforms. In one embodiment, Butterworth filters are used forpreprocessing: for monopole data, Butterworth filters with two bands areused, with bands picked as [1,5] kHz, and [5,12] kHz; and for dipoledata, three frequency bands are used, namely: [1,2.5] kHz, [2.5,5.5]kHz, and [5.5,12] kHz respectively. The plots of the Butterworth filtersare illustrated in FIGS. 6a and 6b showing three Butterworth filterswith different cutoff frequencies on the normalized frequency scale inFIG. 6a and on the original frequency scale in FIG. 6 b.

STC 2D Images

One manner of (pre-)processing the acoustic array data (at 102) is theslowness time coherence (STC) approach described in co-owned C. V.Kimball and T. L. Marzetta, “Semblance processing of borehole acousticarray data,” Geophysics Vol. 49, No. 3, (March 1984) pp. 274-281; U.S.Pat. No. 4,594,691 to Kimball et al., entitled “Sonic Well Logging”, andS. Bose, et al., “Semblance criterion modification to incorporate signalenergy threshold,” SEG Annual Meeting (2009), each of which is herebyincorporated by reference herein in its entirety. Although this approachis normally used in dispersive waves, for non-dispersive waves, it canbe processed non-dispersively by bandpass filtering the data viamultiple frequency bands. See, V. Rama Rao and M. N. Toksoz, “Dispersivewave analysis—method and applications,” Earth Resources LaboratoryIndustry Consortia Annual Report, MIT, 2005, which is herebyincorporated by reference herein in its entirety. Thus, STC processingmay still be used after bandpass filtering.

Standard STC processing generally involves taking the data of amulti-receiver sonic tool, stacking the moveout-corrected receiveroutputs by depth level and identifying selected peaks of a coherencemeasure of the result, and producing logs of sonic properties of theformation versus borehole depth on the basis of selected parameters ofthe peaks. More particularly, the generation of STC 2D images isexplained in detail in the previously incorporated publications toKimball et al., and to S. Bose et al. Examples of STC 2D images areillustrated in the top portions of FIGS. 19-23, where the first rowshows the STC 2D images from two different frequency bands of monopoledata and from three different frequency bands of dipole data. In FIGS.19-23, the x axis denotes the slowness in μs/ft, while the y axisdenotes the time in μs. The value of each pixel (typically representedby color or shade) is called “semblance”.

STC 1D Projection

When using Support Vector Machines (SVM) for classification as describedhereinafter, it may be useful to vectorize the STC 2D images. Astraightforward way to vectorize the images is to project STC 2D imagesonto the slowness axis. All that is required is to choose a windowrepresenting primary arrivals for projection and compute the maximumvalue along the time axis for each slowness value and use them as a 1Dvector. In FIG. 7a , a sonic tool is shown gathering data, plots ofwhich are shown in FIG. 7b . An STC 2D image generated from the data ofFIG. 7b is shown in FIG. 7c , with the projection window marked. An STC1D vector generated from a projection of the STC 2D image of FIG. 7c isshown in FIG. 7 d.

Radon Images and Projections

Radon transforms are closely related to standard STC transforms. In STCprocessing, all amplitude information is removed in favor of anormalized semblance which takes values between zero and one, whereas inRadon processing the amplitude information is retained. See, Radon, J.“On the Determination of Functions from their Integral Values AlongCertain Manifolds”, IEEE Transactions on Medical Imaging 5:4 pp. 170-176(1986). Accordingly, standard STC processing may be called a normalizedversion of Radon processing, or conversely, Radon processing may becalled a non-normalized version of standard STC processing. Therefore,for purposes of the specification and claims herein, the term “STC” isto be understood broadly to include Radon processing as well. Forpurposes of brevity, generally only the results of the normalized STCprocessing are set forth.

In embodiments, Radon transforms are used to obtain 2D (“non-normalizedSTC”) maps (images) in one or more frequency bands. In otherembodiments, the 2D maps obtained via Radon transforms may be projectedto obtain a 1D non-normalized STC vector.

Labeling

In embodiments, each 2D (normalized or non-normalized) STC map (orcorresponding STC 1D (normalized or non-normalized) vector projection)in the training set is assigned a label corresponding to the annularcondition (scenario) in which the data was acquired for real data or forgenerated for synthetic data. Examples of such labels were previouslydescribed.

Classification Using Support Vector Machines

In machine learning, Support Vector Machine (SVM) is a supervisedlearning model with associated learning algorithms which analyze dataused for binary class classification and regression. The presentdisclosure, however, deals with a multiclass classification problem.Thus, a strategy of one-to-all multiclass SVM may be utilized at 108.See, C.-W. Hsu and C.-J. Lin, “A comparison of methods for multiclasssupport vector machines.” IEEE Trans Neural Network, Vol. 13, No. 2, pp.415-425, (2002).

Assume a training set is available with 1 samples paired with theirlabels as: (x₁,y₁), . . . , (x_(l),y_(l)), where x_(i)∈{1, . . . , l}are the training sets and y_(i)ε{1, . . . , l} are the labels. The m-thSVM solves the following problems:

$\begin{matrix}{{{\min\limits_{w^{m},b^{m},c^{m}}{\frac{1}{2}\left( w^{m} \right)^{T}w^{m}}} + {C{\sum\limits_{i = 1}^{l}ɛ_{i}^{m}}}}{{{{{s.t.\mspace{14mu} \left( w^{m} \right)^{T}}{\varphi \left( x_{i} \right)}} + b^{m}} \geq {1 - ɛ_{i}^{m}}},\mspace{14mu} {{{if}\mspace{14mu} y_{i}} = m},{{{\left( w^{m} \right)^{T}{\varphi \left( x_{i} \right)}} + b^{m}} \leq {ɛ_{i}^{m} - 1}},\mspace{14mu} {{{if}\mspace{14mu} y_{i}} = m},{ɛ_{i}^{m} \geq 0},\mspace{14mu} {i = 1},\ldots \mspace{14mu},l,}} & (1)\end{matrix}$

where the training data x_(i) are mapped to a higher dimensional spaceby the function ϕ, w^(m) and b^(m) are the SVM weight and biascoefficients respectively, ε^(m) are margin coefficients in a penaltyterm CΣ_(i=1) ^(l)ε_(l) ^(m) with a penalty parameter C and thesuperscript T represents the transposed quantity. The penalty term isused to address the general case when data is not linearly separable.The coefficients are estimated as part of the learning process byminimizing the expression in equation 1. After solving it, there are kpossible decision functions: (w¹)^(T)ϕ(x)+b¹, . . . ,(w^(k))^(T)ϕ(x)+b^(k). It may be said that x belongs to the class whichhas the largest value of the decision function:

$\begin{matrix}{{{class}\mspace{14mu} {of}\mspace{14mu} (x)} \equiv {\underset{{m = 1},\; \ldots \;,\; k}{\arg \; \max}\left( {{\left( w^{m} \right)^{T}{\varphi (x)}} + b^{m}} \right)}} & (2)\end{matrix}$

Full Frequency Band STC 2D and STC 1D Data Classification Using SupportVector Machine Classifier

Various combinations of full frequency band monopole and dipole dataused for training and testing are analyzed. For example, Table 3provides a summary of the monopole data sets used for training andvalidation, while Table 5 provides a summary of the dipole data setsused for training and validation. The monopole data sets include: cleandata (no noise added to the waveforms); and data with additive noise(SNR=1 dB, and SNR=10 dB). Data cubes 1:2:25 were used for training, andcubes 2:2:24 for validation. In Table 3, classification rate (averagedover all 5 labels) is reported on the cross-validation (CV) dataset.Additionally, included are examples where only one cube (with noisy orclean data) was used for training.

TABLE 3 Summary of monopole datasets used for training and validation.Classification rate is computed on validation dataset. MONOPOLE DATATrain/Model Validation Classification Dataset Dataset Rate on CV dataclean data clean data 1 clean data SNR1 0.2 clean data SNR10 0.2 SNR1clean data 0.945 SNR1 SNR1 0.735 SNR1 SNR10 1 SNR10 clean data 0.8 SNR10SNR1 0.9994 SNR10 SNR10 0.9917 clean data, 1 cube clean data 1 cleandata, 1 cube SNR1 0.2 clean data, 1 cube SNR10 0.2 SNR1, 1 cube cleandata 0.6372 SNR1, 1 cube SNR1 0.9863 SNR1, 1 cube SNR10 0.9194 SNR10, 1cube clean data 0.5806 SNR10, 1 cube SNR1 0.6422 SNR10, 1 cube SNR10 1

The learned models are used to classify the unlabeled data for twoscenarios of interests (Scenario 1, and Scenario 2), with ground truthlabels designed as in Table 2. Classification rates corresponding to thetwo scenarios are provided in Table 4.

TABLE 4 Classification of two unlabeled monopole datasets (Scenario 1and 2). Classification rate is computed based on ground truth labelsfrom Table 2. MONOPOLE DATA Classification Classificaton Model datasetTest set Rate Test set rate clean data scene 1, clean data 1 scene 2,clean data 1 clean data scene 1, SNR1 0 scene 2, SNR1 0.375 clean datascene 1, SNR10 0 scene 2, SNR1 0.375 SNR1 scene 1, clean data 1 scene 2,clean data 0.75 SNR1 scene 1, SNR1 1 scene 2, SNR1 1 SNR1 scene 1, SNR101 scene 2, SNR10 0.995 SNR10 scene 1, clean data 1 scene 2, clean data0.75 SNR10 scene 1, SNR1 1 scene 2, SNR1 1 SNR10 scene 1, SNR10 1 scene2, SNR10 0.995 clean data, 1 cube scene 1, clean data 1 scene 2, cleandata 1 clean data, 1 cube scene 1, SNR1 0 scene 2, SNR1 0.375 cleandata, 1 cube scene 1, SNR10 0 scene 2, SNR10 0.375 SNR1, 1 cube scene 1,clean data 0.6750 scene 2, clean data 0.75 SNR1, 1 cube scene 1, SNR10.98 scene 2, SNR1 1 SNR1, 1 cube scene 1, SNR10 1 scene 2,SNR10 0.86SNR10, 1 cube scene 1, clean data 0.62 scene 2, clean data 0.75 SNR10, 1cube scene 1, SNR1 0.73 scene2, SNR1 0.775 SNR10, 1 cube scene 1, SNR101 scene 2, SNR10 1

The same method is utilized with respect to the dipole source data, andreport classification rates on cross-validation, and test set data areset forth in Tables 5 and 6.

FIG. 8 is a classification result (map) using SVM on unlabeled fullfrequency band monopole data for Scenario 1 over a depth of interest.FIG. 9 is a classification result (map) using SVM on unlabeled fullfrequency band monopole data for Scenario 2 over a depth of interest.FIG. 10 is a classification result (map) using SVM on unlabeled fullfrequency band dipole data for Scenario 1 over a depth of interest. FIG.11 is a classification result (map) using SVM on unlabeled fullfrequency band dipole data for Scenario 2 over a depth of interest.

TABLE 5 Summary of dipole datasets used for training and validation.Classification rate is computed on validation dataset. DIPOLE DATATrain/Model Validation Classification Dataset Dataset Rate on CV dataclean data clean data 1 clean data SNR1 0.4228 SNR1 clean data 1 SNR1SNR1 0.9983 clean data, 1 cube clean data 1 clean data, 1 cube SNR10.4461 SNR1, 1 cube clean data 0.9878 SNR1, 1 cube SNR1 0.9561

TABLE 6 Classification of two unlabeled dipole datasets (Scenario 1 and2). Classification rate is computed based on ground truth labels fromTable 2. DIPOLE DATA Classification Test set Model Dataset Test set RateRate Classification clean data scene 1, clean data 1 scene 2, clean data1 clean data scene 1, SNR1 0.61 scene 2, SNR1 0.39 SNR1 scene 1, cleandata 1 scene 2, SNR1 1 SNR1 scene 1, SNR1 1 scene 2, SNR1 1 clean data,1 cube scene 1, clean data 1 scene 2, clean data 1 clean data, 1 cubescene 1, SNR1 0.565 scene 2, SNR1 0.315 SNR1, 1 cube scene 1, clean data1 scene 2, clean data 1 SNR1, 1 cube, scene 1, clean data 0.995 scene 2,SNR1 0.965

Multiband STC 2D and STC 1D Data Classification Using Support VectorMachines

In one aspect, classification results can be improved by usingButterworth filters. As previously mentioned, STC is a non-dispersiveprocessing approach, so the data may be band-passed through multiplefrequency bands such that the output of each band can be processednon-dispersively. Classification rates for each label of Scenario 1 andScenario 2 are reported separately in Table 7.

Frequency ranges for monopole and dipole data may be selected asfollows. For monopole data, Butterworth filters with two frequency bandsare used: BPF1=[1,5] kHz, and BPF2=[5,12] kHz. For dipole data, threefrequency bands are used; BPF1=[1,2.5] kHz, BPF2=[2.5,5.5] kHz, andBPF3=[5.5,12] kHz. Additionally, the data from monopole and dipole canbe jointly combined within these frequency bands to enhance the SVMclassifier (see Table 7).

TABLE 7 Classification results for CV dataset and Scenario 1 andScenario 2 using multiband monopole and dipole data. Data used fortraining falls in one of the groups of multiband data: for monopolesource, BPF1 = [1, 5] kHz, and BPF2 = [5, 12] kHz, and for dipole data,three frequency bands are BPF1 = 1, 2.5], BPF2 = [2.5, 5.5] kHz, andBPF3 = [.5, 12] kHz. Classification Rate per ClassificationClassification Dataset Label (1-5) on CV Data Rate-Scene 1 Rate-Scene 2MONO BPF1 1, 1, 1, 1, 1 1 1 MONO BPF2 1, 1, 1, 1, 1 1 1 DIP BPF1 0.9867,0.94, 0.9267, 0.92 0.97 0.76, 0.9807 DIP BPF2 1, 1, 1, 1, 1 1 1 DIP BPF31, 1, 1, 1, 1 1 1 MONO BPF1-2 1, 1, 1, 1, 1 1 1 DIP BPF 1-3 1, 1, 1, 1,1 1 1 MONO + DIP 1, 1, 1, 1, 1 1 1

FIGS. 12 and 13 show classification maps over the depth interval ofinterest. More particularly, FIG. 12 shows classification results usingmonopole bandpass filter 1 (MONO BPF1) (e.g., STC-1D) data (panel 1),monopole BPF2 data (panel 2), dipole BPF1 data (panel 3), monopole BPF2data (panel 4), monopole BPF3 data (panel), all monopole bands (MONOBPF1-2) (panel 6), all dipole bands (DIP BPF1-3) (panel 7), and allmonopole and dipole bands (panel 8), all for Scenario 1. Similarly, FIG.13 shows classification results using monopole BPF1 data (panel 1),monopole BPF2 data (panel 2), dipole BPF1 data (panel 3), monopole BPF2data (panel 4), monopole BPF3 data (panel), all monopole bands (MONOBPF1-2) (panel 6), all dipole bands (DIP BPF1-3) (panel 7), and allmonopole and dipole bands (panel 8), all for Scenario 2.

Feature Extractors

According to embodiments, feature extractors such as auto-encoders andMel-Frequency Cepstral Coefficients (MFCC) may be used in combinationwith Support Vector Machines for classification.

Auto-Encoders

An auto-encoder is an artificial neural network for learning efficientrepresentations. It consists of two parts: an encoder and a decoder.See, e.g., F. Chollet, “Building autoencoders in keras,” in The KerasBlog (2016). Because massive training datasets are not necessarily beingutilized, an auto-encoder will be designed using all the datasetsavailable (the test sets and the training sets) for learning betterfeatures.

The mappings of the encoder and decoder are defined as:

ϕ:χ→ρ and ψ:ρ→χ.

The features p generated from the auto encoder are called bottleneckfeatures which will also be sent to the decoder for reconstruction.Then, all that is required is to find the parameters for the followingoptimization problem:

$\begin{matrix}{\left( {\overset{\sim}{\varphi},\overset{\sim}{\psi}} \right) = {\underset{\varphi,\psi}{\arg \; \min}{{X - {\left( {\psi \cdot \varphi} \right)X}}}_{2}^{2}}} & (3)\end{matrix}$

The goal of the auto-encoder is to learn a representation (coding) froma data set and is also used for dimensionality reduction. While aprincipal component analysis (PCA) can only have linear mappings,auto-encoders can have nonlinear encodings as well. Unlike PCA,auto-encoders can be easily extended as a stacked PCA. Some auto-encodervariations include an denoising auto-encoder, a sparse auto-encoder, avariational Bayes auto-encoder and a convolutional auto-encoder. In FIG.14, a convolutional auto-encoder is illustrated with only convolutionaland pooling layers and without the fully connected layers.

The parameters of the auto-encoder of FIG. 14 (starting from an image)are shown on FIG. 15, and the dimension of the bottleneck features canbe tuned by using a different number of (max)pooling layers, where themaximum value of the values of pixels within a window is used torepresent the window. If a decrease in dimension is desired, morepooling layers are required.

FIGS. 16a-16e show learned bottleneck features for monopole bandpassfilter 1 (BPF1) (for STC-2D) data, monopole BPF2 data, dipole BPF1 data,dipole BPF2 data, and dipole BPF3 data respectively, with the x-axisbeing the pixel index of the bottleneck feature, and the y-axisrepresenting the training set index.

In one embodiment, auto-encoding followed by SVM is utilized fortraining at 108 of FIG. 1. This combination falls into the class ofsemi-supervised learning methods. FIG. 17 shows a diagram for trainingand testing, and FIG. 18 shows a diagram for cross-validation. As seenin FIG. 17, the features are learned from the labeled data as well asthe unlabeled scenario data. To increase the number of samples, all theunlabeled data sets are also used as the input to the auto encoder inthe training step. More particularly, FIG. 17 shows an illustration ofthe step for an example where the STC-2D maps for all the 750 samples inthe training set along with the 200 samples each from scenario 1 and 2are fed from the testing set to the auto-encoder to arrive at a muchlower dimensional learned feature set. This process is repeated for eachof the bandpass filtered STC maps for monopole and dipole data. Thelearned features of the bands and modes are then jointly fed into an SVMwhich is trained and cross-validated using the labels from the trainingset as shown in FIG. 18. The trained SVM can now be applied to thefeatures extracted from the testing set to complete the classification.

FIGS. 19-23 show examples of initial (original) and the reconstructedSTC 2D images for the two different monopole bands and three differentdipole bands generated by the convolutional auto-encoder of FIG. 15.Thus, FIG. 19 shows the original and reconstructed images for label oneof a first cube; FIG. 20 shows the original and reconstructed images forlabel two of a second cube; FIG. 21 shows the original and reconstructedimages for label three of a third cube; FIG. 22 shows the original andreconstructed images for label four of a fourth cube; and FIG. 23 showsthe original and reconstructed images for label five of a fifth cube. Itwill be appreciated that for some purposes, the reconstructed images arereasonable representations of the original images.

Supplying the bottleneck features of the auto-encoder to the SVM,classification maps over depth interval of interest are generated forthe two test sets respectively in FIG. 24 and FIG. 25. In each figure,classification results are shown for eight modalities: monopole BPF1,monopole BPF2, dipole MPF1, dipole MPF2, dipole MPF3, monopole BPF1-2,dipole BPF1-3, and combined monopole BPF1-2 and dipole BPF1-3.Classification rates on the cross-validation set and unlabeled multibandmultimodality data are in Table 8.

TABLE 8 Classification results using AE + SVM on cross-validation setand two unlabeled multiband multimodality datasets. Data used forAutoencoder features falls in one of the groups of multiband data: formonopole source, BPF1 = [1, 5] kHz, and BPF2 = [5, 12] kHz, and fordipole data, 3 frequency bands are BPF1 = [1, 2.5] kHz, BPF2 = [2.5,5.5] kHz, and BPF3 = [5.5, 12] kHz. AE + SVM Classification Rate perClassification Classification Dataset Label (1-5) on CV Data Rate-Scene1 Rate-Scene 2 MONO BPF1 1, 0.993, 0.993, 1, 0.98 1 1 MONO BPF2 1, 1, 1,1, 1 1 1 DIP BPF1 0.913, 0.753, 0.573, 0.705 0.75 0.473, 0.793 DIP BPF20.98, 0.98, 0.993, 0.973, 0.986 0.99 0.99 DIP BPF3 1, 1, 1, 1, 1 1 1MONO BPF1-2 1, 1, 1, 1, 1 1 1 DIP BPF1-3 1, 0.953, 0.98, 0.96, 0.980.985 0.99 MONO + DIP 1, 0.953, 0.993, 0.967, 0.98 0.985 0.99

FIGS. 26a-26h depict support vectors corresponding to various multibandmodalities for the five labels of interest for the monopole BPF1 data,the monopole BPF2 data, the dipole BPF1 data, the dipole BPF2 data, thedipole BPF3 data, the aggregate monopole BPF1-2 data, the aggregatedipole BPF1-3 data, and the aggregate of all monopole and dipole data.

Mel-Frequency Cepstral Coefficients (MFCC)

MFCC are known in the literature as Mel-frequency cepstral coefficients.See, e.g., K. Prahalad, “Speech technology: A practical introduction,”Carnegie Mellon University & International Institute of InformationTechnology Hyderabad PPT, (2003). They are widely used for signalclassification and speech recognition. In one embodiment, for a trainingdataset, MFCC may be used as the features for a SVM classifier. Thesefeatures can be generated through the following steps.

First, the short time Fourier transform (a windowed excerpt) is appliedto a signal:

X[k]=DFT(x[n])  (4)

The powers of the spectrum obtained above are mapped onto the Mel scalethrough:

$\begin{matrix}{{{Mel}(f)} = {2595 \times {\log_{10}\left( {1 + \frac{f}{700}} \right)}}} & (5)\end{matrix}$

Next, triangular overlapping windows are used and logs of the powers ateach of the mel frequencies are taken,

$\begin{matrix}{{Y\lbrack m\rbrack} = {\log \left( {\sum\limits_{k = f_{m - 1}}^{f_{m + 1}}{{{X\lbrack k\rbrack}}^{2}{B_{m}\lbrack k\rbrack}}} \right)}} & (6) \\{{B_{m}\lbrack k\rbrack} = \left\{ \begin{matrix}0 & \; \\{\frac{k - f_{m - 1}}{f_{m} - f_{m - 1}},} & {k \in \left\lbrack {f_{m - 1},f_{m}} \right\rbrack} \\{\frac{f_{m + 1} - k}{f_{m + 1} - f_{m}},} & {k \in \left\lbrack {f_{m},f_{m + 1}} \right\rbrack}\end{matrix} \right.} & (7)\end{matrix}$

The last step involves taking the discrete cosine transform for the listof Mel log powers, as if it were a signal (see, S. Young, et al., TheHTK Book (Version 3.4), Cambridge University Engineering Department,(2006)):

$\begin{matrix}{{c\lbrack n\rbrack} = {\frac{1}{M}{\sum\limits_{m = 1}^{M}{{Y\lbrack m\rbrack}\; {\cos \left( \frac{\pi \; {n\left( {m - 0.5} \right)}}{M} \right)}}}}} & (8)\end{matrix}$

The MFCC are the amplitudes of the resulting spectrum after liftering(filtering in the cepstral domain) (see, S. Young, et al. The HTK Book(Version 3.4), Cambridge University Engineering Department, (2006)),

$\begin{matrix}{{c^{\prime}\lbrack n\rbrack} = {\left( {1 + {\frac{L}{2}\sin \frac{\pi \; n}{L}}} \right) \times {{c\lbrack n\rbrack}.}}} & (9)\end{matrix}$

MFCC is a time frequency representation. One can vectorize the 2D MFCCfeatures when using SVM. In one embodiment, MFCCs are generated fromeach waveform. The frame duration may be set at 2.6 ms, with 1 ms set asthe frame shift. By way of example, 30 filterbank channels and 22cepstral coefficients (the number of cepstral coefficients should beless than the number of filterbank channels) are chosen. The lower andupper frequency limits are set to 2000 and 10000 Hz, and the cepstralsine lifter parameter is 2000 (2000 is a default value in MFCCsprocessing).

Some classification results are shown in FIG. 27. For the monopole data,the classification rate on Scenario 2 data is 1, and classification rateon CV data is 0.9987, which breaks down as: classification rate equal to1 for labels 1-4, and classification rate of 0.993 for label 5. For theaggregate dipole data, the classification rate on Scenario 2 data is0.995, and classification rate on CV data is 0.9973, which breaks downas: classification rate equal to 1 for labels 1, 2, 3, and 5, andclassification rate of 9866 for label 4. Finally, for combined monopoleand dipole modalities (Mod MD scene 2), all above mentioned rates areequal to 1.

Classification Using Convolutional Neural Networks (CNN)

Convolutional neural network (CNN) can be used for image recognition,video classification, semantic segmentation, and object localization. ACNN consists of multiple layers of neurons which can process portions ofthe input images called receptive fields. The outputs of thesecollections are then tiled so that their input regions overlap. Forbetter representation, this is repeated for each layer. Tiling allowsCNN to deal with translations of the input data. Compared to multilayerperceptron (MLP), CNN does not suffer from dimensionality, and scaleswell to higher resolution images. It has the following distinguishingfeatures: 3D volumes of neurons, local connectivity and shared weights.These properties allow CNN to achieve better generalization on computervision problems.

CNN Parameters

For purposes of the machine learning module implementing CNN on STCimages. in order to reduce the computation burden, according toembodiments, the STC 2D images may be downsampled, e.g., to 40%. Then,the downsampled images may be cropped and fed into the CNN. As suggestedby FIG. 28, separate CNNs for the monopole and the dipole data may bedesigned. Each training sample can be a 2D image or a 3D tensor. By wayof example only, 400 neurons may be used in the first fully-connected(FC) layer and 450 neurons for monopole and dipole data separately. InFIG. 28, two convolutional layers are shown applied with a receptivefield of size of each neuron being 3*3. A single max pooling layer isshown. Except for the situation where STC 2D images are utilized, MFCCsand bottleneck features can also be put into the CNN. In the nextsection, we will show how to combine the information from differentmodalities.

Visualization of CNN

For purposes of illustrating CNN visualization results, the dipole databased CNN model is used as an example. A specific arrangement of a CNNis shown in FIG. 29 corresponding to FIG. 28 where three 2D STC mapssize 240×78 are scanned by a 3*3(*3) window to convolutional layer 1(size 238×76×25). A similar window of 3*3*25 is scanned to convolutionallayer 2 (size 236×74×25), and a max pool layer is used to reduce theinput into the fully connected layer to 118×37×25. The fully connectedlayer is shown (in this case) to provide three output classes withassociated weights, it being appreciated that in other embodiments,different numbers of classes may be generated. The highest weight valueis then selected (as suggested by equation (2)) as the determined label(answer product). The multiband sample STC 2D data (maps) which areinput into the CNN is shown in FIG. 30a , and the filter weightscomputed from convolutional layer 1 operation are shown in FIG. 30b .The weights look like edge detectors which can detect edges fromdifferent angles. To observe the activation map, a training sample fromlabel 3 in FIG. 30b is selected and the activation maps fromconvolutional layers 1 and 2 are plotted separately. The activation mapsseem to be the combination of those three STC 2D images, and they areshown in FIG. 31a and FIG. 31 b.

Comparing activation map 1 of FIG. 31a and activation map 2 of FIG. 31b, the features in activation map2 appear much sharper. For monopoledata, similar STC 2D input maps and filter weights are shown in FIGS.32a and 32b , while similar activation maps are shown in FIGS. 33a and33 b.

Joint Training with 2 Streams

According to one aspect, three frameworks (embodiments) are provided forcombining the features from monopole and dipole data, all based on CNNs.As seen in FIG. 34, a first type of CNN (denoted by CNN T1) adds (sums)the outputs from fully connected layers from different modalities (e.g.,monopole and dipole) together before feeding into another fullyconnected layer. The second type of CNN (denoted by CNN T2) concatenatesthe fully connected layers from monopole and dipole modalities. Thethird type of CNN (denoted by CNN T3) also concatenates the fullyconnected layers from the monopole and dipole modalities but adds onemore fully connected layer based on the second type of CNN, for furtherdimension reduction.

For a fast implementation of CNNs, an integrated development environmentcomposed of Anaconda (a free and open source distribution of the Pythonand R programming languages, Theano (a Python library that permitsdefining, optimization, and evaluation of mathematic expressions), andKeras (a higher level library which operates over Theano andstream-lines the process of building deep learning networks) may beused. To run the auto-encoder, OPENBLAS (or BLAS) library may be used.

Turning now to FIGS. 37a and 37b , results for different CNNclassifications for scenarios 1 and 2 respectively are shown side byside. Thus, in each figure, the left-most plot shows results for CNNwhere the input is two-band monopole STC data, and from left to right,the next plots show results for three-band dipole STC data, and combinedstreams using summation of monopole and dipole (T1), concatenation ofmonopole and dipole (T2), and concatenation plus an additional fullyconnected layer (T3). It may be concluded that in the synthetic datacase, all CNN-based classifiers give perfect classification.

In one aspect, the CNN model parameters, such as the convolutionalfilter parameters are trained by optimizing an objective functionsimilar to equation (1) using stochastic descent algorithms.

Some of the methods and processes described above, including, but notlimited to the STC processing and the machine learning module, can beperformed by a processor. The term “processor” should not be construedto limit the embodiments disclosed herein to any particular device typeor system. The processor may include a computer system. The computersystem may also include a computer processor (e.g., a microprocessor,microcontroller, digital signal processor, or general purpose computer)for executing any of the methods and processes described above.

The computer system may further include a memory such as a semiconductormemory device (e.g., a RAM, ROM, PROM, EEPROM, or Flash-ProgrammableRAM), a magnetic memory device (e.g., a diskette or fixed disk), anoptical memory device (e.g., a CD-ROM), a PC card (e.g., PCMCIA card),or other memory device.

Some of the methods and processes described above, can be implemented ascomputer program logic for use with the computer processor. The computerprogram logic may be embodied in various forms, including a source codeform or a computer executable form. Source code may include a series ofcomputer program instructions in a variety of programming languages(e.g., an object code, an assembly language, or a high-level languagesuch as C, C++, or JAVA). Such computer instructions can be stored in anon-transitory computer readable medium (e.g., memory) and executed bythe computer processor. The computer instructions may be distributed inany form as a removable storage medium with accompanying printed orelectronic documentation (e.g., shrink wrapped software), preloaded witha computer system (e.g., on system ROM or fixed disk), or distributedfrom a server or electronic bulletin board over a communication system(e.g., the Internet or World Wide Web).

Alternatively or additionally, the processor may include discreteelectronic components coupled to a printed circuit board, integratedcircuitry (e.g., Application Specific Integrated Circuits (ASIC)),and/or programmable logic devices (e.g., a Field Programmable GateArrays (FPGA)). Any of the methods and processes described above can beimplemented using such logic devices.

Although only a few example embodiments have been described in detailabove, those skilled in the art will readily appreciate that manymodifications are possible in the example embodiments without materiallydeparting from this invention. By way of example only, while particularexamples were given of labels for specific combinations of states forthe inner and outer annuli of a well, labels for other states andcombinations thereof may be utilized such as a label for an innerannulus and an outer annulus of said annuli being filled with cement, alabel for the inner annulus being filled with water and the outerannulus being filled with cement, a label for the inner annulus beingfilled with cement and the outer annulus being filled with water, and alabel for the inner and outer annuli being filled with water. Also, byway of example only, while CNNs having a particular window sizes andparticular numbers of convolutional layers, maxpool layers, and fullyconnected layers were described, it will be appreciated that the CNNsmay be constructed with different window sizes, and different numbers oflayers. Accordingly, all such modifications are intended to be includedwithin the scope of this disclosure as defined in the following claims.In the claims, means-plus-function clauses are intended to cover thestructures described herein as performing the recited function and notonly structural equivalents, but also equivalent structures. Thus,although a nail and a screw may not be structural equivalents in that anail employs a cylindrical surface to secure wooden parts together,whereas a screw employs a helical surface, in the environment offastening wooden parts, a nail and a screw may be equivalent structures.It is the express intention of the applicant not to invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of the claims herein, exceptfor those in which the claim expressly uses the words ‘means for’together with an associated function.

1. A method of characterizing the status of annuli of a multiple-casedwell of interest, comprising: utilizing a dataset of labeled slownesstime coherence (STC) samples obtained from processing at least one of(i) synthesized sonic data and (ii) measured sonic data obtained from amultiple-cased well, training a machine learning module to receive STCsample inputs and provide output labels for a plurality of states forannuli of a multiple-cased well; locating a sonic tool having at leastone transmitter and multiple detectors at a location in the well ofinterest; firing the at least one transmitter, and detecting with themultiple detectors the resulting sonic waveforms impacted by annuli ofthe well of interest; preprocessing the sonic waveforms to obtain atleast one STC map; providing the at least one STC map as the STC sampleinputs of the machine learning module to obtain an indication of thestatus of the annuli of the multiple-cased well adjacent the location ofthe sonic tool.
 2. The method of claim 1, wherein said machine learningmodule implements at least one of a convolutional neural network (CNN),a support vector machine (SVM), and an auto-encoder.
 3. The method ofclaim 1, wherein said preprocessing the sonic waveforms comprisesbandpass filtering said sonic waveforms into at least two bands andconducting STC processing on each band separately.
 4. The method ofclaim 1, wherein said at least one transmitter includes a monopoletransmitter and a dipole transmitter and said preprocessing the sonicwaveforms comprises separately filtering sonic waveforms resulting fromwaves detected as a result of the firing of the monopole transmitter andwaves detected as a result of the firing of the dipole transmitter. 5.The method of claim 4, wherein said preprocessing the sonic waveformscomprises separately bandpass filtering the sonic waveforms resultingfrom waves detected as a result of the firing of the monopoletransmitter into at least two bands, and separately bandpass filteringthe sonic waveforms resulting from waves detected as a result of thefiring of the dipole transmitter into at least two bands.
 6. The methodof claim 1, wherein said machine learning module implements a CNN, saidpreprocessing the sonic waveforms to obtain at least one STC mapcomprises preprocessing the sonic waveforms to obtain at least one 2DSTC map and said at least one 2D STC map is provided as the STC sampleinputs to the CNN by scanning a window over pixels of the at least one2D STC map.
 7. The method of claim 6, wherein said preprocessing thesonic waveforms comprises bandpass filtering said sonic waveforms intoat least two bands and conducting STC processing on each band separatelysuch that said at least one 2D STC map comprises a plurality of 2D STCmaps corresponding to each band.
 8. The method of claim 6, wherein saidat least one transmitter includes a monopole transmitter and a dipoletransmitter and said preprocessing the sonic waveforms comprisesseparately filtering sonic waveforms resulting from waves detected as aresult of the firing of the monopole transmitter and waves detected as aresult of the firing of the dipole transmitter and separately bandpassfiltering the sonic waveforms resulting from waves detected as a resultof the firing of the monopole transmitter into at least two bands andseparately bandpass filtering the sonic waveforms resulting from wavesdetected as a result of the firing of the dipole transmitter into atleast two bands and conducting STC processing on each band separatelysuch that said at least one 2D STC map comprises a plurality of 2D STCmaps corresponding to each band.
 9. The method of claim 8, wherein theCNN includes a plurality of convolutional layers, at least one maximumpooling layer, and at least one fully connected layer.
 10. The method ofclaim 9, wherein the CNN has a first set of convolutional layers and afully connected layer for 2D STC maps corresponding to the data from themonopole transmitter, and a second set of convolutional layers and fullyconnected layer for 2D STC maps corresponding to the data from thedipole transmitter, results of the fully connected layer for the datafrom the monopole transmitter and results of the fully connected layerfor the data from the dipole transmitter being summed in the fullyconnected layer which provides said indication of the status of theannuli of the multiple-cased well.
 11. The method of claim 9, whereinthe CNN has a first set of neural network convolutional layers for 2DSTC maps corresponding to the data from the monopole transmitter, asecond set of neural network convolutional layers for 2D STC mapscorresponding to the data from the dipole transmitter, and a fullyconnected layer where results of the first set and second set of neuralnetworks are concatenated and which provides said indication of thestatus of the annuli of the multiple-cased well.
 12. The method of claim9, wherein the CNN has a first set of neural network convolutionallayers for 2D STC maps corresponding to the data from the monopoletransmitter, a second set of neural network convolutional layers for 2DSTC maps corresponding to the data from the dipole transmitter, a firstfully connected layer where results of the first set and second set ofneural networks are concatenated, and a second fully connected layerthat receives the output of the first fully connected layer and providessaid indication of the status of the annuli of the multiple-cased well.13. The method of claim 1, wherein said machine learning moduleimplements a SVM, said preprocessing the sonic waveforms to obtain atleast one STC map comprises preprocessing the sonic waveforms to obtaina 1D STC vector map and said 1D STC vector map is provided as the STCsample inputs to said SVM.
 14. The method of claim 13, wherein saidpreprocessing the sonic waveforms comprises bandpass filtering saidsonic waveforms into at least two bands and conducting STC processing oneach band separately such that said at least one 1D STC vector mapcomprises a plurality of 1D STC vector maps corresponding to each band.15. The method of claim 13, wherein said at least one transmitterincludes a monopole transmitter and a dipole transmitter, and saidpreprocessing the sonic waveforms comprises separately filtering sonicwaveforms resulting from waves detected as a result of the firing of themonopole transmitter and waves detected as a result of the firing of thedipole transmitter and separately bandpass filtering the sonic waveformsresulting from waves detected as a result of the firing of the monopoletransmitter into at least two bands, and separately bandpass filteringthe sonic waveforms resulting from waves detected as a result of thefiring of the dipole transmitter into at least two bands and conductingSTC processing on each band separately such that said at least one 1DSTC vector map comprises a plurality of 1D STC vector maps correspondingto each band.
 16. The method of claim 1 wherein said machine learningmodule implements an auto-encoder, said preprocessing the sonicwaveforms to obtain at least one STC map comprises preprocessing thesonic waveforms to obtain either a 1D STC vector map or a 2D STC mapwhich is provided as the STC sample inputs to said auto-encoder.
 17. Themethod of claim 16, wherein said auto-encoder includes a bottleneckwhere bottleneck features are defined and said machine learning modulefurther implements an SVM where said bottleneck features are provided asinputs to said SVM.
 18. The method according to claim 1, furthercomprising: moving the sonic tool to another location in the well ofinterest, and repeating said firing, preprocessing and providing inorder to obtain an indication of the status of the annuli of themultiple-cased well adjacent the other location of the sonic tool. 19.The method according to claim 18, further comprising: using theindications of the status of the annuli of the multiple-cased well,making a decision regarding remedial action with respect to the well ofinterest.
 20. The method according to claim 1, wherein said outputlabels for said plurality of states for annuli include a label for aninner annulus and an outer annulus of said annuli being filled withcement, a label for the inner annulus being filled with water and theouter annulus being filled with cement, a label for the inner annulusbeing filled with cement and the outer annulus being filled with water,and a label for the inner and outer annuli being filled with water. 21.The method of claim 1, wherein said labeled STC samples are labelednormalized STC samples and said preprocessing the sonic waveforms toobtain at least one STC map comprises preprocessing to obtain at leastone normalized STC map which is provided as sample inputs.
 22. Themethod of claim 1, wherein said labeled STC samples are labelednon-normalized STC samples and said preprocessing the sonic waveforms toobtain at least one STC map comprises preprocessing to obtain at leastone non-normalized STC map which is provided as sample inputs.
 23. Amethod of characterizing the status of annuli of a multiple-cased wellof interest, comprising: measuring and/or synthesizing multimodal sonicdata of a borehole having a plurality of casings with annuli surroundingthe casing; preprocessing the sonic data in multiple frequency bands toobtain 2D or 1D slowness time coherence (STC) maps for each mode of saidmultimodal sonic data; generating labels that correspond to combinationsof designated possible states of the annuli surrounding the casing usingat last one of (i) cement evaluation maps, (ii) expert interpretation,and (iii) synthetic scenarios; from said STC maps and said labels,creating a dataset of labeled STC samples for said multiple frequencybands; using said dataset of labeled STC samples, training a machinelearning module to receive STC sample inputs and provide output labelsfor a plurality of states for annuli of a multiple-cased well, whereinthe machine learning module comprises at least one of a convolutionalneural network (CNN), a support vector machine (SVM), and anauto-encoder; locating a sonic tool having at least a monopoletransmitter, a dipole transmitter and multiple detectors in the well ofinterest; firing the monopole and dipole transmitters, and detectingwith the multiple detectors the resulting sonic waveforms impacted byannuli of the well of interest; preprocessing the sonic waveforms toobtain STC maps resulting from the monopole and dipole firings; andproviding the STC maps as the STC sample inputs of the machine learningmodule to obtain an indication of the status of the annuli of themultiple-cased well.
 24. The method according to claim 23, furthercomprising: moving the sonic tool to another location in the well ofinterest, and repeating said firing, preprocessing and providing inorder to obtain an indication of the status of the annuli of themultiple-cased well adjacent the other location of the sonic tool. 25.The method according to claim 24, further comprising: using theindications of the status of the annuli of the multiple-cased well,making a decision regarding remedial action with respect to the well ofinterest.